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The paper provides global optimization algorithms for two particularlydifficult nonconvex problems raised by hybrid system identification: switchinglinear regression and bounded-error estimation. While most works focus on localoptimization heuristics without global optimality guarantees or with guaranteesvalid only under restrictive conditions, the proposed approach always yields asolution with a certificate of global optimality. This approach relies on abranch-and-bound strategy for which we devise lower bounds that can beefficiently computed. In order to obtain scalable algorithms with respect tothe number of data, we directly optimize the model parameters in a continuousoptimization setting without involving integer variables. Numerical experimentsshow that the proposed algorithms offer a higher accuracy than convexrelaxations with a reasonable computational burden for hybrid systemidentification. In addition, we discuss how bounded-error estimation is relatedto robust estimation in the presence of outliers and exact recovery undersparse noise, for which we also obtain promising numerical results.

Global optimization for low-dimensional switching linear regression and bounded-error estimation